I'm attaching a blend here. At the left of the screen you can see the original object and at the right, the exported-imported one.
Notice that the imported object has like faceted / triagulated faces when subsurf is on.
According to a friend of mine, this could be caused by the normal export options in fbx. He says that there should be an option for not exporting smooth normals.
I really don't know if that makes sense to you, but well, there is definitely an issue with normals here.